This paper aims at Takagi - Sugeno (TS) fuzzy controllers as gain scheduling (GS) schemes of PID controllers. A TS fuzzy controller employs arbitrary input fuzzy sets, product or Zadeh fuzzy logic AND, TS fuzzy rules ...This paper aims at Takagi - Sugeno (TS) fuzzy controllers as gain scheduling (GS) schemes of PID controllers. A TS fuzzy controller employs arbitrary input fuzzy sets, product or Zadeh fuzzy logic AND, TS fuzzy rules with linear consequent, and the generalized defuzzifler containing the popular centrold defuzzifler as a special case. We first establish the relationship between the TS fuzzy controller and the linear PID controller. The TS ftizzy controller is accurately a nonlinear PID controller with gains continuously changing with Its process output. Then we point out that the TS fuzzy controller is closely related to the traditional gain scheduler. The gains of the TS ftizzy controller are determined by three two - Input - one - output fuzzy systems with singleton output fuzzy sets. Finally, as a demonstration, a simple TS fuzzy controller employing two linear input fuzzy sets, Zadeh fuzzy logic AND, and the popular centrold defuzzifler is designed to be the gain scheduler for the PID controller.展开更多
The analytical structure of a class of typical Takagi Sugeno (TS) fuzzy controllers is revealed in this paper.The TS fuzzy controllers consist of three or more trapezoidal input fuzzy sets, Zadeh fuzzy logic AND opera...The analytical structure of a class of typical Takagi Sugeno (TS) fuzzy controllers is revealed in this paper.The TS fuzzy controllers consist of three or more trapezoidal input fuzzy sets, Zadeh fuzzy logic AND operator,fuzzy rules with linear consequent, and the centriod defuzzifier. The TS fuzzy controllers are proved to be accurately nonlinear PID controllers with gains continuously changing with process output. The analytical expressions of the variable gains of the TS fuzzy controllers are derived and their mathematical characteristics including the bounds and geometrical shape of the gain variation are analyzed. The resulting explicit structures show that the TS fuzzy controllers are inherently nonlinear PID gain scheduling controllers with variable gains in different regions of input space.展开更多
文摘This paper aims at Takagi - Sugeno (TS) fuzzy controllers as gain scheduling (GS) schemes of PID controllers. A TS fuzzy controller employs arbitrary input fuzzy sets, product or Zadeh fuzzy logic AND, TS fuzzy rules with linear consequent, and the generalized defuzzifler containing the popular centrold defuzzifler as a special case. We first establish the relationship between the TS fuzzy controller and the linear PID controller. The TS ftizzy controller is accurately a nonlinear PID controller with gains continuously changing with Its process output. Then we point out that the TS fuzzy controller is closely related to the traditional gain scheduler. The gains of the TS ftizzy controller are determined by three two - Input - one - output fuzzy systems with singleton output fuzzy sets. Finally, as a demonstration, a simple TS fuzzy controller employing two linear input fuzzy sets, Zadeh fuzzy logic AND, and the popular centrold defuzzifler is designed to be the gain scheduler for the PID controller.
基金Supported by the National Science Foundation(Grant No.69874038)
文摘The analytical structure of a class of typical Takagi Sugeno (TS) fuzzy controllers is revealed in this paper.The TS fuzzy controllers consist of three or more trapezoidal input fuzzy sets, Zadeh fuzzy logic AND operator,fuzzy rules with linear consequent, and the centriod defuzzifier. The TS fuzzy controllers are proved to be accurately nonlinear PID controllers with gains continuously changing with process output. The analytical expressions of the variable gains of the TS fuzzy controllers are derived and their mathematical characteristics including the bounds and geometrical shape of the gain variation are analyzed. The resulting explicit structures show that the TS fuzzy controllers are inherently nonlinear PID gain scheduling controllers with variable gains in different regions of input space.
